To calculate: The least common denominator for the pair of expressions frac{x + 3}{x^{2} + 20x 100} and frac{3}{2x^{2} + 20x}

Kyran Hudson 2021-01-31 Answered
To calculate: The least common denominator for the pair of expressions x + 3x2 + 20x 100 and 32x2 + 20x
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Expert Answer

rogreenhoxa8
Answered 2021-02-01 Author has 109 answers
The least common denominator for the pair of expressions x + 3x2 + 20x 100 and 32x2 + 20x is 2x(x + 10)2.
Given Information:
The provided expressions are, x + 3x2 + 20x 100 and 32x2 + 20x.
Formula used:
The least common denominator (LCD) of two or more rational expressions is calculated as follows:
Step 1: Find the factors of the denominators.
Step 2: Multiply all the unique prime factors with their highest power from all the denominators. The product would be the LCD.
Calculation:
Consider the provided expressions, x + 3x2 + 20x 100 and 32x2 + 20x.
First factor the denominators of the rational expressions as,
x2 + 20x + 100=(x + 10)(x + 10)
And,
2x2 + 20x=2x(x + 10)
Now, consider the product of each factor raised to its highest power, which is the LCD. Hence, the least common denominator is, 2x(x + 10)2
Therefore, the least common denominator for the pair of i 2 expressions
x + 3x2 + 20x + 100 and 32x2 + 20x is 2x(x + 10)2
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